Question 471367
I'll do the first one to get you started. If that doesn't help, feel free to ask me further.


# 1


{{{((11y-44)/10)/((y-4)/(6y))}}} Start with the given expression.



{{{((11y-44)/10)*(6y/(y-4))}}} Multiply the first upper fraction by the reciprocal of the lower fraction. In other words, flip the second fraction and multiply.



{{{(6y(11y-44))/(10(y-4))}}} Multiply the fractions by multiplying the corresponding numerators and denominators separately. Note: I rearranged the 6y term a bit. 



{{{(6y*11(y-4))/(10(y-4))}}} Factor {{{11y-44}}} to get {{{11(y-4)}}}



{{{(2*3y*11(y-4))/(10(y-4))}}} Factor {{{6}}} to get {{{2*3}}}



{{{(2*3y*11(y-4))/(2*5(y-4))}}} Factor {{{10}}} to get {{{2*5}}}



{{{(highlight(2)*3y*11*highlight((y-4)))/(highlight(2)*5y*highlight((y-4)))}}} Highlight the common terms (shared between the numerator and denominator)



{{{(cross(2)*3y*11*cross((y-4)))/(cross(2)*5y*cross((y-4)))}}} Cancel out the common terms (shared between the numerator and denominator)



{{{(3*11y)/(5)}}} Simplify



{{{(33y)/5}}} Multiply 3 and 11 to get 33.



So {{{((11y-44)/10)/((y-4)/(6y))}}} completely simplifies to {{{(33y)/5}}}



In other words, {{{((11y-44)/10)/((y-4)/(6y))=(33y)/5}}}